At the height of the US offensive in late 2010, commanders chose what they considered their best option: They approved an airstrike that flattened all the buildings in town, more than 40, including Mohammad’s home. Though no civilians were killed, the bombardment quickly became one of the most controversial attacks of the war in Afghanistan.

Three years later, the village is a sandy ruin, symbolizing the gains and losses of America’s longest war. A handful of villagers, Mohammad among them, have trickled back. The US Army withdrew this summer from the valley where Tarok Kolache is located. The Taliban have mostly fled to other districts.

Relative peace came to Tarok Kolache, but only after it was demolished.

‘‘What did we win in this war? We lost our homes. We lost our village,’’ said Mohammad, 47, the village’s de facto patriarch, with thick black eyebrows and a wavy beard. ‘‘The Taliban do not live here anymore, but they were only fighting in the first place because the Americans were here.’’

On the other side of the world, the man who decided to bomb Tarok Kolache, Army Colonel David Flynn, sits in his office at a base in Oklahoma, hoping his ‘‘painstaking choice’’ has paid off.

‘‘I think about Tarok Kolache every day,’’ Flynn said. ‘‘There were no good options there.’’

To compensate the villagers for the loss of their 100-year-old homes, the US military built them square, concrete rooms. But those structures — oddities in a valley of mud-baked dwellings — are already cracking. Locals refuse to live in them, so the buildings sit empty, the subject of mockery.

There are still the barbed wire and blast barriers brought here to protect the US base at the edge of the village, constructed after the Tarok Kolache bombing. The base itself has been dismantled.

Mostly, there are sand, rocks, and empty space where there once were homes. Some residents received up to $10,000 in compensation from the US military and moved elsewhere. Some said it was too dangerous to stay in Tarok Kolache after the US base was established. Many claimed the Americans failed to rebuild what they had promised.

Mohammad and his fellow villagers say they were never supportive of the Taliban; the insurgents had chased or scared many of them out of their homes. But he claims the series of events that ended with the destruction of his village started with the American invasion in 2001. ‘‘If the Americans hadn’t come, we would still have our village,’’ he said.

The bombing didn’t kill any civilians, but it stood out for the scale of its destruction. US officials were quick to call the operation a success. Afghan members of the US-backed government said it was tragic but necessary. Both groups pointed to the proof: The Taliban left Tarok Kolache.

Flynn watched as the airstrike was carried out, knowing it would weaken the enemy but infuriate many locals. He thinks his decision, supported by top American commanders, was the right one.

‘‘Leadership isn’t about being the most popular guy on the street,’’ he said. ‘‘It’s about getting the job done and improving a bad environment.’’

There were objections not only from Afghan civilians but also from American academics and analysts, who said it was an example of the unnecessary use of force. For some outside the military, Tarok Kolache became a symbol of the Afghan war’s poor execution.

Mohammad learned about the American debate over Tarok Kolache months after it began raging on blogs and op-ed pages. After asking a friend to Google the name of his village, he couldn’t believe what he saw — a seemingly endless back-and-forth about whether Tarok Kolache’s destruction was justified.

‘‘It was amazing — I didn’t know we were famous in Tarok Kolache,’’ he said, smiling.

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